1. Field of the Invention
The present invention relates in general to the field of information processing, and more specifically to a system and method for protecting overload of look-ahead delta sigma modulators using overload anticipation technology.
2. Description of the Related Art
Many signal processing systems include delta sigma modulators to quantize an input signal into one or more bits. Delta sigma modulators trade-off increased noise in the form of quantization error in exchange for high sample rates and noise shaping. Delta-sigma modulators are particularly useful for modulating low frequency signal, such as audio signal, because delta-sigma modulators include a noise shaping loop filter that includes a noise transfer function (“NTF”) that modulates a significant amount of noise out of an audio signal baseband. An audio signal baseband is approximately zero (0) Hz to twenty-five (25) kHz. In-band noise decreases as oversampling of input signal sample x(n) increases. Higher order loop filters also decrease in-band noise. “Delta-sigma modulators” are also commonly referred to using other interchangeable terms such as “sigma-delta modulators”, “delta-sigma converters”, “sigma delta converters”, and “noise shapers”.
FIG. 1 depicts a delta-sigma modulator 100 that receives an input signal sample x(n), determines a difference between x(n) and the delayed output signal y(n−1), processes the difference signal with a noise shaping loop filter 102, and quantizes the filter 102 output with quantizer 104 to provide output signal y(n). The quantizer 104 can provide multi-bit or one-bit quantization. The quantizer step size, A, represents the difference between each quantization level. One-bit quantizers have only two quantization levels specified as {−Δ/2, Δ/2} or {−1,1}. Shreier and Temes, Understanding Delta-Sigma Signal Converters, IEEE Press, 2005 describes conventional delta-sigma modulators in more detail.
Delta-sigma modulators, especially delta-sigma modulators with 1-bit quantizers, are prone to overload. Quantizer overload generally occurs when a quantizer 104 receives an input signal that is either excessively high or low. Quantizer input signals that exceeds the upper and lower quantization levels of quantizer 104 will cause quantizer 104 to overload. Additionally, multi-order (i.e. delta-sigma modulators with multi-order loop filters) delta-sigma modulator systems exhibit an increasingly lower tolerance to an input signal that does not exceed yet approaches the upper and lower quantization levels of the quantizer. Quantizer overload causes state variables of loop filter 102 to grow without bound, and, thus, the delta-sigma modulator output signal y(n) will no longer represent input signal sample x(n). Quantizer overload causes many undesirable effects. In audio systems, quantizer overload can result in instability and cause oscillations resulting in undesirable, audible tones. Quantizer overload can also cause abrupt signal magnitude and frequency changes, which also result in undesirable noise.
Quantizer overload is more likely to occur when the input signal x(n) is large relative to the full scale feedback signal y(n−1) because the negative feedback of signal y(n−1) will be unable to compensate for the large value of input signal x(n). A “modulation index” (“MI”) is defined as the ratio of the maximum input signal x(n) to the maximum feedback signal (max(x(n))/max(y(n−1))). Designers of one-bit delta-sigma modulators generally attempt to limit the MI of one-bit delta-sigma modulators to 0.5. In other terms, a delta-sigma modulator input signal sample x(n) that produces 75%+1 outputs y(n) and 25%−1 outputs y(n) would have a modulation index of 0.5 or 50% (75%−25%=50%).
Some applications specify a full-scale input signal by the MI. For example, the super audio compact disk (“SACD”) specification defines a full-scale input signal as one having a modulation index of 50%. However, it is desirable to handle larger input signals, such as transient signals, without overloading the delta-sigma modulator.
Higher order loop filters and more aggressive noise shaping also increase the susceptibility of delta-sigma modulators to quantizer overload. FIG. 2 depicts a noise versus frequency plot 300 for a conventional delta sigma modulator. At the upper baseband frequency, fB, the NTF of the delta sigma modulator effectively lowers the noise magnitude, thus increasing the signal-to-noise ratio (“SNR”). However, as noise in the baseband is further suppressed, noise magnitudes outside the baseband continue to increase. Thus, more aggressive noise shaping can result in larger signals and increase the probability of quantizer overload. The steepness of the noise versus frequency plot 300 outside of the baseband is directly related to the noise shaping gain of delta sigma modulator loop filter.
The susceptibility to quantizer overload represents a key design constraint in the design of delta-sigma modulators. High MI and high SNR both run counter to good delta sigma modulator stability.
Look-ahead delta sigma modulators have been shown to improve quantizer overload performance and allow for more aggressive noise shaping. FIG. 3 depicts a look-ahead delta sigma modulator 300 having a depth of N. The depth N refers to the number of sequential samples that are processed by look-ahead delta sigma modulator 300 to determine a single output y(n). X(N)t represents a vector for time t whose elements are the N input samples used to determine a single output y(n), X(N)t={x(n), x(n+1), . . . , x(n+N−1)}t for time t. The Look-ahead/Actual Output ‘Switch’ is a functional representation indicating that during look-ahead operations, each output candidate vectors Yi is provided as simulated feedback data, Y={y(n−1), y(n−2), . . . , y(n−N−1)}. “i” represents the number of possible output candidate vectors. For a one-bit delta sigma modulator, each element of the output candidate vector can be a logical −1 or +1. Thus, for an N element vector, there are 2N possible combinations of vectors, and i=2N. For each time t, the state variables of P-order loop filter 306 from the previous, actual quantization operation are saved. The saved state variables are used as the initial state variables each time the look-ahead delta sigma modulator 300 sequentially quantizes each element of input signal vector X(N)t using each element of the ith output candidate vector Yi as sequential feedback. The P-order loop filter 306 has an order of P and filter coefficients c0, c1, . . . , cP-1. The order and filter coefficient values are a matter of design choice and are generally chosen with regard to the NTF, signal transfer function (“STF”), SNR, and stability.
After processing each input signal vector X(N)t and each set of output candidate vectors Yi, the quantizer 304 determines which output candidate vector Yi represents the best match with the input signal vector X(N)t. The best match output candidate vector is referred to as the best match output candidate vector Ybestm. One embodiment of a “best match” is described by Hiroshi Kato, “Trellis Noise-Shaping Converters and 1-bit Digital Audio,” AES 112th Convention, May 10–13, 2002 Munich, as the match having the lowest cost in terms of root mean square (“RMS”) power. Conventional research in look-ahead modulators primarily involves two threads. Additional conventional look-ahead delta sigma modulator information can be found in Hiroshi Kato, Japanese Patent JP, 2003-124812 A, Harpe, P., Reefman D., Janssen E., “Efficient Trellis-type Sigma Delta Modulator,” AES 114th Convention, Mar. 22–25, 2003 Amsterdam (referred to herein as “Harpe”); James A. S. Angus, “Tree Based Look-ahead Sigma Delta Modulators,” AES 114th Convention, Mar. 22–25, 2003 Amsterdam; James A.S. Angus, “Efficient Algorithms for Look-Ahead Sigma-Delta Modulators,” AES 155th Convention, Oct. 10–13, 2003 New York; and Janssen B., Reefman D., “Advances in Trellis based SDM structures,” AES 115th Convention, Oct. 10–13, 2003 New York.
The actual output y(n) is chosen as the leading bit of the output candidate vector Yi determined to be the best match. The Look-ahead/Actual Output Switch 302 then feeds back the chosen output delayed by one unit of time y(n−1) to update the state variables of P-order loop filter 306 with actual state variables.
Computation and storage requirements conventionally grow exponentially with increases in the look-ahead depth. Schemes have been developed to prune trellis-type look-ahead delta sigma modulators, but pruning can miss the most important paths for overload protection. Thus, look-ahead delta sigma modulators continue to be subject to quantizer overload.